Ambartsumyan S.A. Theory of anisotropic plates

Technomic Publishing Co., Inc. 1970. - 255 pp. – (Progress in Materials Science Series. Vol. II), OCR.This book is devoted to the development and formulation of an improved theory of anisotropic plates free from the basic hypothesis of the classical theory, i.e., from the hypothesis of nondeformable normals. The versions of the improved theory considered in this book are, in fact, new approaches for the consideration of the effect of transverse displacements and of normal stresses with respect to the middle-plate surface. These versions introduce a basic correction to the classical theory and may be applied in the derivation of the first correction to the basic stress state of the classical theory. The magnitude of this correction increases together with the ratio Ei/Gi3 and may be significant for highly anisotropic plates.
The book consists of four chapters. The first chapter presents information from the theory of elasticity of the anisotropic body which is needed for further presentation of the material. The second chapter presents two improved theories of anisotropic plates based upon the principal statements of the theory of elasticity of the anisotropic body. These theories are based on hypotheses which impose limitations only on transverse stress-deformation characteristics of the plate. The third chapter considers numerous problems regarding the determination of stresses and displacements of different types of anisotropic plates with different forms of loading. The fourth chapter is devoted to problems of stability and vibration. Free and forced vibrations, static and dynamic stability, and supersonic flutter of different types of anisotropic and transversely isotropic plates are considered here. Numerous examples show that the classical theory of anisotropic plates is imperfect in many cases and the results obtained using this theory are not always acceptable in many important applied problems. There are 24 tables, 30 figures and 98 references in this book.